Random strain effects on the coupled magnetic and nematic transitions of iron-based superconductors

Magnetism and nematicity in the iron pnictides provide an interesting example of intertwined phases, with the vestigial nematic phase characterized by an order parameter that is composite in the primary magnetic order parameters. As a result, phenomena impacting one phase will inevitably be manifested in the other phase as well. For instance, structural disorder in the form of random strain, ubiquitously present in quantum materials, act simultaneously as a random nematic field and a random magnetic exchange. Due to its dual character, the impact of random strain is expected to go beyond the random-field Ising model effects that it enforces on the nematic degrees of freedom alone.  Here, we propose the random-Baxter-field Ashkin-Teller model as a minimal model to capture the interplay between random strain, magnetism, and nematicity in the iron pnictides. Using Replica-Exchange Wang Landau Monte Carlo simulations, we find that random strain disorder introduces different length and time scales for the magnetic and nematic domains. Moreover, it induces magnetic correlations that are absent in the clean system, manifested by enhanced fluctuations with an emergent enlarged symmetry. Our results demonstrate that random strain disorder in intertwined phases leads to richer physics than in systems where the nematic order is the sole instability of the system.